Complex Shape Not Correctly Unwrapping
The easier is to unwrap with 'project from view with bounds' :
That gives you a flat projection of your 3D model into the UV map part. This projection depends on the 3D view itself, so you may want to align your model correctly (using NumPad4 and NumPad6, for instance). Once done, you may have to adjust (grab and scale) your UV map a bit to fit your image.



Note : I took the wrong image from your screen captures, that why you still see the UVs from this image in the gif above even when the unwrap is done.